Underestimation of Standard Errors in Multi-Site Time Series Studies

Multi-site time series studies of air pollution and mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating acute effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and estimate pooled air pollution effects taking into account both within-site statistical uncertainty, and across-site heterogeneity. Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, highly correlated predictors, non linear confounding etc.) make modelling all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to be combined. In this paper we investigate the impact of variance underestimation on the pooled relative rate estimate. We focus on two-stage normal-normal hierarchical models and on under- estimation of the statistical variance at the first stage. By mathematical considerations and simulation studies, we found that variance underestimation does not affect the pooled estimate substantially. However, some sensitivity of the pooled estimate to variance underestimation is observed when the number of sites is small and underestimation is severe. These simulation results are applicable to any two-stage normal-normal hierarchical model for combining information of site-specific results, and they can be easily extended to more general hierarchical formulations. We also examined the impact of variance underestimation on the national average relative rate estimate from the National Morbidity Mortality Air Pollution Study and we found that variance underestimation as much as 40% has little effect on the national average.

Development of record-breaking statistics for climatological time-series analysis

The number of record-breaking events expected to occur in a strictly stationary time-series depends only on the number of values in the time-series, regardless of distribution. This holds whether the events are record-breaking highs or lows and whether we count from past to present or present to past. However, these symmetries are broken in distinct ways by trends in the mean and variance. We define indices that capture this information and use them to detect weak trends from multiple time-series. Here, we use these methods to answer the following questions: (1) Is there a variability trend among globally distributed surface temperature time-series? We find a significant decreasing variability over the past century for the Global Historical Climatology Network (GHCN). This corresponds to about a 10% change in the standard deviation of inter-annual monthly mean temperature distributions. (2) How are record-breaking high and low surface temperatures in the United States affected by time period? We investigate the United States Historical Climatology Network (USHCN) and find that the ratio of record-breaking highs to lows in 2006 increases as the time-series extend further into the past. When we consider the ratio as it evolves with respect to a fixed start year, we find it is strongly correlated with the ensemble mean. We also compare the ratios for USHCN and GHCN (minus USHCN stations). We find the ratios grow monotonically in the GHCN data set, but not in the USHCN data set. (3) Do we detect either mean or variance trends in annual precipitation within the United States? We find that the total annual and monthly precipitation in the United States (USHCN) has increased over the past century. Evidence for a trend in variance is inconclusive.

The Time-Series Properties on Housing Prices: A Case Study of the Southern California Market

We examine the time-series relationship between housing prices in eight Southern California metropolitan statistical areas (MSAs). First, we perform cointegration tests of the housing price indexes for the MSAs, finding seven cointegrating vectors. Thus, the evidence suggests that one common trend links the housing prices in these eight MSAs, a purchasing power parity finding for the housing prices in Southern California. Second, we perform temporal Granger causality tests revealing intertwined temporal relationships. The Santa Anna MSA leads the pack in temporally causing housing prices in six of the other seven MSAs, excluding only the San Luis Obispo MSA. The Oxnard MSA experienced the largest number of temporal effects from other MSAs, six of the seven, excluding only Los Angeles. The Santa Barbara MSA proved the most isolated in that it temporally caused housing prices in only two other MSAs (Los Angels and Oxnard) and housing prices in the Santa Anna MSA temporally caused prices in Santa Barbara. Third, we calculate out-of-sample forecasts in each MSA, using various vector autoregressive (VAR) and vector error-correction (VEC) models, as well as Bayesian, spatial, and causality versions of these models with various priors. Different specifications provide superior forecasts in the different MSAs. Finally, we consider the ability of theses time-series models to provide accurate out-of-sample predictions of turning points in housing prices that occurred in 2006:Q4. Recursive forecasts, where the sample is updated each quarter, provide reasonably good forecasts of turning points.

Snow and ice surfaces on King George Island (Antarctic Peninsula) with high-resolution TerraSAR-X time series, with links to shapfiles and GeoTIFFs

Changes of glaciers and snow cover in polar regions affect a wide range of physical and ecosystem processes on land and in the adjacent marine environment. In this study, we investigate the potential of 11-day repeat high-resolution satellite image time series from the TerraSAR-X mission to derive glaciological and hydrological parameters on King George Island, Antarctica during the period Oct/25/2010 to Apr/19/2011. The spatial pattern and temporal evolution of snow cover extent on ice-free areas can be monitored using multi-temporal coherence images. SAR coherence is used to map glacier extent of land terminating glaciers with an average accuracy of 25 m. Multi-temporal SAR color composites identify the position of the late summer snow line at about 220 m above sea level. Glacier surface velocities are obtained from intensity feature-tracking. Surface velocities near the calving front of Fourcade Glacier were up to 1.8 ± 0.01 m/d. Using an intercept theorem based on fundamental geometric principles together with differential GPS field measurements, the ice discharge of Fourcade Glacier was estimated to 20700 ± 5500 m**3/d (corresponding to ~19 ± 5 kt/d). The rapidly changing surface conditions on King George Island and the lack of high-resolution digital elevation models for the region remain restrictions for the applicability of SAR data and the precision of derived products.

The C37 alkenone record of sea water of time series station DYNAPROC

The concentrations of suspended particulate pigments, C37-C38 alkenones, total organic carbon and nitrogen in the Ligurian Sea (northwestern Mediterranean) have been studied at 5 and 30 m depth during well defined thermocline conditions. An accurate description of the short term changes of these compounds has been achieved by means of four 36-h sampling cycles each encompassing consecutive filtration periods of 4 h. During sampling the thermocline changes were followed closely by simultaneous measurements of water column temperature, salinity and other physical parameters. The analysis of the collected samples indicates that the Haptophyte pigments and alkenones are essentially synthesized at the levels of highest primary production and therefore the C37 alkenone record reflects the seawater temperature at this depth level. The study also shows that part of these alkenones are distributed throughout the water column in association to the suspended particles. This process results in C37 alkenone distributions that, due to their high resistance to chemical and microbial degradation, record the temperature of the highest primary productivity layers even at shallow (e.g., 5 m depth) or deep (e.g., 1100 m depth) waters.

Collection of data on plant height along the plant diversity gradient in the Jena Experiment (Main Experiment, time series since 2002)

This data set contains a time series of plant height measurements (vegetative and reproductive) from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In addition, data on species specific plant heights for the main experiment are available from 2002. In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. 1. Plant height was recorded, generally, twice a year just before biomass harvest (during peak standing biomass in late May and in late August). Methodologies of measuring height have varied somewhat over the years. In earlier year the streched plant height was measured, while in later years the standing height without streching the plant was measured. Vegetative height was measured either as the height of the highest leaf or as the length of the main axis of non-flowering plants. Regenerating height was measured either as the height of the highest flower on a plant or as the height of the main axis of flowering. Sampled plants were either randomly selected in the core area of plots or along transects in defined distances. For details refer to the description of individual years. Starting in 2006, also the plots of the management experiment, that altered mowing frequency and fertilized subplots (see further details in the general description of the Jena Experiment) were sampled. 2. Species specific plant height was recorded two times in 2002: in late July (vegetative height) and just before biomass harvest during peak standing biomass in late August (vegetative and regenerative height). For each plot and each sown species in the species pool, 3 plant individuals (if present) from the central area of the plots were randomly selected and used to measure vegetative height (non-flowering indviduals) and regenerative height (flowering individuals) as stretched height. Provided are the means over the three measuremnts per plant species per plot.

Aboveground community and species-specific plant biomass from the Jena Experiment (Main Experiment, time series since 2002)

This data set comprises a time series of aboveground community plant biomass (Sown plant community, Weed plant community, Dead plant material, and Unidentified plant material; all measured in biomass as dry weight) and species-specific biomass from the sown species of the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. Aboveground community biomass was harvested twice a year just prior to mowing (during peak standing biomass twice a year, generally in May and August; in 2002 only once in September) on all experimental plots of the main experiment. This was done by clipping the vegetation at 3 cm above ground in up to four rectangles of 0.2 x 0.5 m per large plot. The location of these rectangles was assigned by random selection of new coordinates every year within the core area of the plots (i.e. the central 10 x 15 m). The positions of the rectangles within plots were identical for all plots. The harvested biomass was sorted into categories: individual species for the sown plant species, weed plant species (species not sown at the particular plot), detached dead plant material (i.e., dead plant material in the data file), and remaining plant material that could not be assigned to any category (i.e., unidentified plant material in the data file). All biomass was dried to constant weight (70°C, >= 48 h) and weighed. Sown plant community biomass was calculated as the sum of the biomass of the individual sown species. The data for individual samples and the mean over samples for the biomass measures on the community level are given. Overall, analyses of the community biomass data have identified species richness as well as functional group composition as important drivers of a positive biodiversity-productivity relationship.

Reference list of 120 datasets from time series station Payerne used for exploratory search

The analysis of time-dependent data is an important problem in many application domains, and interactive visualization of time-series data can help in understanding patterns in large time series data. Many effective approaches already exist for visual analysis of univariate time series supporting tasks such as assessment of data quality, detection of outliers, or identification of periodically or frequently occurring patterns. However, much fewer approaches exist which support multivariate time series. The existence of multiple values per time stamp makes the analysis task per se harder, and existing visualization techniques often do not scale well. We introduce an approach for visual analysis of large multivariate time-dependent data, based on the idea of projecting multivariate measurements to a 2D display, visualizing the time dimension by trajectories. We use visual data aggregation metaphors based on grouping of similar data elements to scale with multivariate time series. Aggregation procedures can either be based on statistical properties of the data or on data clustering routines. Appropriately defined user controls allow to navigate and explore the data and interactively steer the parameters of the data aggregation to enhance data analysis. We present an implementation of our approach and apply it on a comprehensive data set from the field of earth bservation, demonstrating the applicability and usefulness of our approach.

Aboveground community and species-specific plant biomass from the Jena Experiment (Dominance Experiment, time series since 2002)

This data set comprises a time series of aboveground community plant biomass (Sown plant community, Weed plant community, Dead plant material, and Unidentified plant material; all measured in biomass as dry weight) and species-specific biomass from the sown species of the dominance experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the dominance experiment, 206 grassland plots of 3.5 x 3.5 m were established from a pool of 9 species that can be dominant in semi-natural grassland communities of the study region. In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 3, 4, 6, and 9 species). Plots were maintained by bi-annual weeding and mowing. Aboveground community biomass was harvested twice a year, generally in May and August (in 2002 only once in September) on all experimental plots of the dominance experiment. This was done by clipping the vegetation at 3 cm above ground in two rectangles of 0.2 x 0.5 m per experimental plot. The location of these rectangles was assigned by random selection of new coordinates every year within the central area of the plots (excluding an outer edge of 50cm). The positions of the rectangles within plots were identical for all plots. The harvested biomass was sorted into categories: individual species for the sown plant species, weed plant species (species not sown at the particular plot), detached dead plant material, and remaining plant material that could not be assigned to any category. Biomass was dried to constant weight (70°C, >= 48 h) and weighed. Sown plant community biomass was calculated as the sum of the biomass of the individual sown species. The mean of both samples per plot and the individual measurements are provided in the data file. Overall, analyses of the community biomass data have identified species richness and the presence of particular species as an important driver of a positive biodiversity-productivity relationship.